We investigate the distribution of neutron star masses in different populations of binaries, employing Bayesian statistical techniques. In particular, we explore the differences in neutron star masses between sources that have experienced distinct evolutionary paths and accretion episodes. We find that the distribution of neutron star masses in non-recycled eclipsing high-mass binaries as well as of slow pulsars, which are all believed to be near their birth masses, has a mean of 1.28 M and a dispersion of 0.24 M . These values are consistent with expectations for neutron star formation in core-collapse supernovae. On the other hand, double neutron stars, which are also believed to be near their birth masses, have a much narrower mass distribution, peaking at 1.33 M , but with a dispersion of only 0.05 M . Such a small dispersion cannot easily be understood and perhaps points to a particular and rare formation channel. The mass distribution of neutron stars that have been recycled has a mean of 1.48 M and a dispersion of 0.2 M , consistent with the expectation that they have experienced extended mass accretion episodes. The fact that only a very small fraction of recycled neutron stars in the inferred distribution have masses that exceed ∼2 M suggests that only a few of these neutron stars cross the mass threshold to form low-mass black holes.